A multi-criteria decision problem generally involves choosing one of a number alternatives based on how
well those alternatives rate against a chosen set of criteria. The criteria themselves are weighted in
terms of importance to the decision maker, and the overall "score" of an alternative is the
weighted sum of its rating against each criteria. The ordering of the alternatives by their decision
scores is taken to be their ranking by preference.

The Analytic Hierarchy Process allows users to assess the relative weight of multiple criteria
(or multiple alternatives against a given criterion) in an intuitive manner. Its major innovation was
the introduction of pairwise comparisons. Pairwise comparisons is a metod that is informed by research
showing that when quantitative ratings are unavailable, humans are still adept at recognizing whether
one criteria is mor important than another. Dr. Thomas Saaty, the inventor of the AHP methodology,
established a consistent way of converting such "pairwise" comparisons (X is more important
than Y) into a set of numbers representing the relative priority of each of the criteria.

A potential drawback with the AHP method is "Rank Reversal". Because judgments in AHP are
relative by nature, changing the set of alternatives may change the decision scores of all the
alternatives. It was shown that even if a new, very poor alternative is added to a completed model, the
alternatives with top scores sometimes reverse their relative ranking.

In the Simple Multi-Attribute Rating Technique, ratings of alternatives are assigned directly, in the
natural scales of the criteria (where available). For instance, when assessing the criterion "top
speed" for motor cars, a natural scale would be a range of 100 to 200 miles per hour. In order to
keep the weighting of criteria and rating of alternatives as separate as possible, the different scales of
criteria need to be converted to a common internal scale. In AHP this is taken care of by the relative
nature of the rating technique. In SMART, this is done mathematically by the decision maker by means of a
"Value Function".

The simplest choice of a value function is a linear function, and in most cases this is sufficient.
However, to better capture human psychology in decision making, it is often advantageous to use
non-linear functions. Utility Theory offers a deep and complex literature for choosing value functions.

The Advantage of SMART: The decision model is independent of the alternatives. While the introduction
of value functions somewhat complexifies the decision modeling process, the advantage is that the
ratings of alternatives are not relative, so that changing the number of alternatives considered will
not in itself change the decision scores of the original alternatives.

We hope that the support Criterium DecisionPlus offers to apply both techniques within the same
package will promote more research on the relative merits of the two methodologies. In the interim, our
tentative guide as to which technique to use is as follows:

AHP

The simplicity of model building in AHP suggests its use where possible. If it is unlikely that new
alternatives will need to be introduced beyond the set under consideration then rank reversal will not
be such a problem.

SMART

If new alternatives are likely to be added to the model after its initial construction, and the
alternatives are amenable to a direct rating approach (not so qualitative as to require pairwise
comparison), then SMART would be a good choice.